The maximum point that the middle of the rope reaches is 75 inches above the ground.
The correct answer is option (A)
What is an amplitude of cosine function?
"An amplitude of the cosine function is the amount by which it varies above and below the x -axis."
For given example,
The height of the middle of the rope, in inches, can be modeled by a cosine function with an amplitude of 36 inches.
⇒ h = 2a cos(x)
with a = 36 inches
If the minimum point that the middle of the rope reaches is 3 inches above the ground,
⇒ h = 2a cos(x) + 3
When the middle of the rope reaches the maximum point, then x = 0
⇒ h = 2 × 36 × cos(0) + 3
⇒ h = 72 × 1 + 3
⇒ h = 72 + 3
⇒ h = 75 inches
Therefore, the maximum point that the middle of the rope reaches is 75 inches above the ground.
The correct answer is option (A)
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